I've looked at the Player Settings and there doesn't seem to be any way to do this, but you could use something like this simple javascript to change the resolution to 1024x768 when the game starts:

function Start () {
Screen.SetResolution(1024, 768, false);
}

This just sets the screen's width to 1024, the screen's height to 768, and sets fullscreen to off, all at the game's start. (Change false to true to turn fullscreen on.)